Sequences Series and Mathematical Induction

Sequences Series and Mathematical Induction
Order 589387
Sequences Series and Mathematical Induction
Sequences
For questions 343 to 345, write the closed formula for the arithmetic sequence.
343. 2, 5, 8, 11, 14, …
344. 6, 4, 2, 0, …
345. , …
For questions 346 and 347, write the recursive formula for the arithmetic
sequence.
346. 2, 5, 8, 11, 14, …
347. 6, 4, 2, 0, …
For questions 348 to 350, write the closed formula for the geometric sequence.
348. 2, 6, 18, 54, …
349. , …
350. 3, –6, 12, –24, …
For questions 351 and 352, write the recursive formula for the geometric
sequence.
351. 2, 6, 18, 54, …
352. , …
353. Given an = 3n 2:
(A) Generate the first four terms of the sequence.
(B) Find a17
.
354. Given
(A) Generate the first four terms of the sequence.
(B) Find a19
.
355. Given an = –2n – 1:
(A) Generate the first four terms of the sequence.
(B) Find a100
.
Sequences Series and Mathematical Induction
356. Given
(A) Generate the first four terms of the sequence.
(B) Find a7
.
357. Given
(A) Generate the first four terms of the sequence.
(B) Find a7
.
For questions 358 to 360, determine whether the given sequence is arithmetic,
geometric, both, or neither.
358. 1, 0.5, 0.25, 0.125, …
359. , 1, …
360. 2,2,2,2, …
361. How many terms are included in the list 2, 7, 12, 17, …, 147?
362. How many terms are included in the list 2, 4, 8, 16, …, 4096?
Series
In questions 363 to 367, use the sequence whose formula is an = 5n – 2. Refer to
the following properties of the summation (sigma) notation, as needed.
363. Write the sum of the first 15 terms, using the sigma notation where the first
two terms have been taken out of the sum.
364. Write the sum of the first n terms, using the sigma notation such that the
summing index begins with 2.
365. Write the sum of the first 15 terms and apply summation notation properties
(a), (b), and (c) to rewrite the sum.
366. Write the extended form of the sum .
367. Compute the sum .
For questions 368 to 372, compute the indicated sum. Refer to the following
special closed formulas, as needed.
where a1
is the first term and an
is the last term of
the arithmetic sequence
, provided r ≠ 1, where a1
is the first term and r is the
common ratio of the geometric sequence
368.
369.
370. 4 7 10 13 16 19 22 25
371. 1 2 4 8 16 32 64 128
372. 3 5 7 9 … 477
Having a hard time figuring out how to do your assignment?
Ask our experts for help and get it done in no time!